Abstract
This chapter examines the classroom implementation of a theoretical framework for the teaching and learning of mathematics—called DNR-based instruction in mathematics—focusing on characteristics of the implementation of DNR to help learners transition between proof schemes. Three episodes from a professional development program for middle and high school teachers are analyzed to reveal the teaching behaviors of an expert DNR instructor. Complexities highlighted include (1) how the instructor balanced the intended mathematical content with the learners’ current understandings, (2) the interplay of the questions whether a result holds and why it holds, and (3) how the instructor created intellectual need for new ideas. As a by-product, learning outcomes of this effort are also examined.KeywordsDNR-based instructionProofProof schemesTheoretical frameworkProfessional development
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